Melt 3 tablespoons of butter in a small microwave-safe bowl and stir in 3 tablespoons granulated sugar, 2 tablespoons brown sugar, and 1 tablespoon of cinnamon until smooth to create the filling.
Trim the crusts from all 8 bread slices using a serrated knife.
Flatten each crustless slice with a rolling pin until it reaches approximately 1/8-inch thickness.
Spread the prepared butter-sugar filling evenly across each flattened bread slice.
Roll each slice tightly into a cylinder.
In a shallow bowl, whisk together the eggs and milk.
Mix the remaining 2 tablespoons of granulated sugar and 2 teaspoons of cinnamon in a separate bowl for the coating.
Heat the remaining 3 tablespoons of butter in a large skillet over medium-high heat.
Dip each roll-up into the egg mixture, ensuring it is well-coated but not soggy.
Place the rolls seam-side down in the hot skillet and sear, turning occasionally, until golden brown on all sides.
Remove from the skillet and immediately roll each piece in the cinnamon-sugar coating mix until fully covered.